Integrally bladed disks (IBDs) are a relatively recent development in gas turbine engine technology. IBDs are bladed disks in which the blades and disk (or hub) form one continuous structure. The blades may be welded to the disk or formed integrally with the disk by being milled from a single block of material. IBDs are also referred to in the aerospace industry as blisks or as integrally bladed rotors (IBRs). While IBDs are becoming more popular in gas turbine aero engines, earlier traditional aero engine designs as well as many current industrial turbine and compressor designs have individual blades that are held in place by inserting them into slots in the disk.
Turbine blades on a bladed disk are part of a dynamic system with a complex vibratory response. For example, consider the difference in the vibratory response of a single turbine blade in isolation and a set of turbine blades mounted to a disk. A single turbine blade in isolation has mode shapes such as first bending and first torsion that generally have broadly spaced natural frequencies, resulting in a relatively simple vibratory response. However, when a set of turbine blades are mounted on a disk, they interact with each other, producing large numbers of modes with closely spaced frequencies and more complex dynamics. A disk with N blades will have N modes with similar frequencies in which the airfoils deflect in a first bending shape, and N modes with similar frequencies in which the airfoils deflect in a first torsion shape. These sets of modes with similar airfoil deflection patterns are referred to as mode families.
Ideally, all of the blades on a single disk are identical to each other, but this is not the case in reality. When it comes to vibration, no two IBDs are alike. Every IBD has a unique set of properties that causes it to vibrate differently from all other bladed disks, even those of the same design. Differences in individual blades due to manufacturing tolerances, wear, damage or repairs will cause them to vibrate at slightly different frequencies. This phenomenon of blades having different frequencies from each other is called mistuning. Because of mistuning and the associated complex vibrational behavior, some blades of an IBD can vibrate strongly while others are not vibrating at all. Blades with a higher vibratory response are more susceptible to high cycle fatigue damage, and because mechanical failure of a bladed disk is such a catastrophic event, there has been a long felt need by operators of turbine engines to be able to predict, and thereby to prevent, vibration-induced damage and associated failures.
Because manufacturing tolerances create part-to-part dimensional variations that have significance regarding an IBD's vibrational performance, it is known to adjust a finite element model (FEM) of an IBD to reflect the actual dimensions of a particular part; i.e. to construct a digital twin of a particular part. Such FEM built to measured dimensions is referred to as a Geometrically Mistuned FEM model. For example, the United States Air Force Research Laboratory presented a paper titled “Automated Finite Element Model Mesh Updating Scheme Applicable to Mistuning Analysis” at the 2014 ASME Turbine Technical Conference and Exposition describing a process for morphing the structured mesh of a nominal finite element model to reflect geometric data collected during an optical scan of an IBD. Other publications addressing this problem include: 1) GT2013-95320 “Uncertainties of an Automated Optical 3D Geometry Measurement, Modeling, and Analysis Process for Mistuned IBR Reverse Engineering”, ASME Turbo Expo 2013; 2) GT2014-26925 “Automated Finite Element Model Mesh Updating Scheme Applicable to Mistuning Analysis”, ASME Turbo Expo 2014; 3) 10.2514/6.2016-1371 “Experimental Validation of an Optically Measured Digital Replica of a Mistuned Rotor Using a System ID Approach”, AAIA SciTech Forum, January 2015; and 4) GT2015-43150 “Experimental Validation of a Mesh Quality Optimized Morphed Geometric Mistuning Model” ASME Turbo Expo 2015. However, when the vibrational behavior predictions of such geometrically mistuned models are compared with experimental results, there remains a difference, most likely due to small residual dimensional measurement errors and possibly also due to small as-built material property variations.
A related problem has been addressed in the medical field where finite element models are used to evaluate how injuries occur in the human body, as discussed in paper IRC-17-107 titled “Development of Morphed Ribcage Finite Element Models for Comparison with PMHS Data” presented at the 2017 International Research Council on Biomechanics of Injury conference. U.S. Pat. No. 9,710,880 B2 titled “User Guided Shape Morphing in Bone Segmentation for Medical Imaging” issued on Jul. 18, 2017. However, the medical field is concerned about static loads on the human body, not high order dynamic loading.
Morphing of models is also useful when identifying objects in an image, as described in U.S. Pat. No. 5,590,261 titled “Finite-Element Method for Image Alignment and Morphing” issued on Dec. 31, 1996. Imaging applications are not concerned with high order vibrational motion.
Process and model refinements over the past few years have continued to improve the correspondence between geometrically mistuned FEM predictions and experimental results for IBD's, but recent evaluations have found that even geometrically mistuned models are unable to predict blade mistuning frequencies for some mode families with a desired degree of accuracy. Because blade vibratory response is so highly sensitive to blade frequency, continued improvement in the analytical modeling of IBDs is desired.